This is a randomized, multicenter study. Patients are stratified into 1 of 3 strata according to extent of residual disease and plans for interval cytoreductive surgery: Stratum A: Optimal (microscopic or macroscopic) residual disease without plans for surgery Stratum B: Suboptimal residual disease without plans for surgery Stratum C: Suboptimal residual disease with plans for surgeryPatients are randomized to 1 of 5 treatment arms. Arm I: Patients receive paclitaxel IV over 3 hours and carboplatin IV over 30 minutes on day 1. Treatment continues every 3 weeks for 8 courses in the absence of disease progression or unacceptable toxicity. Arm II: Patients receive chemotherapy as in arm I and gemcitabine IV over 30 minutes on days 1 and 8. Treatment continues as in arm I. Arm III: Patients receive chemotherapy as in arm I during courses 1-8 and doxorubicin HCl liposome IV over 1 hour on day 1 during courses 1, 3, 5, and 7. Treatment continues as in arm I. Arm IV: Patients receive topotecan IV over 30 minutes on days 1-3 and carboplatin IV over 30 minutes on day 3. Treatment continues every 3 weeks for 4 courses. Patients then receive 4 courses of arm I chemotherapy. Arm V: Patients receive gemcitabine IV over 30 minutes on days 1 and 8 and carboplatin IV over 30 minutes on day 8. Treatment continues every 3 weeks for 4 courses. Patients then receive 4 courses of arm I chemotherapy. Patients with initial unresectable or suboptimal residual disease (more than 1 cm) may undergo interval cytoreductive surgery between courses 4 and 5 of chemotherapy. Patients are followed every 3 months for 2 years and then every 6 months.